Fundamental Concepts ICSE Class-7 Concise Selina Solutions

Fundamental Concepts ICSE Class-7 Concise Selina mathematics Solutions Chapter-11. We provide step by step Solutions of Exercise / lesson-11 Fundamental Concepts ( Including Fundamental Operations ) for ICSE Class-7 Concise Selina Mathematics. Our Solutions contain all type Questions with Exe-11 A , Exe-11 B Exe-11 C , Exe-11 D , Exe-11 E and    Exe-11 F to develop skill and confidence. Visit official Website CISCE for detail information about ICSE Board Class-7.

Fundamental Concepts ICSE Class-7 Concise Selina mathematics Solutions Chapter-11


–: Select Topics :–

 

Exe-11 A,

Exe-11 B,

Exe-11 C,

Exe-11 D,

Exe-11 E,

Exe-11 F,

 


Exercise – 11 A Fundamental Concepts ICSE Class-7 mathematics 

Question 1.

Separate constant terms and variable terms from tile following :
Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-a1

Answer

Constant is only 8 other are variables.

Question 2.

Constant is only 8 others are variables
(i) 2x ÷ 15
(ii) ax+ 9
(iii) 3x2 × 5x
(iv) 5 + 2a-3b
(v) 2y – \frac { 7 }{ 3 } z÷x
(vi) 3p x q ÷ z
(vii) 12z ÷ 5x + 4
(viii) 12 – 5z – 4
(ix) a3 – 3ab2 x c
Answer

(i)

2x ÷ 15 = 2x/15

It is a monomial as it has one term.

(ii)

ax + 9: It is binomial

(∵ It has two terms)

(iii)

3x2 × 5x = 15x3 – It is monomial

(∵ It has one term)

(iv)

5 + 2a – 3b – It is trinomial

(∵ It has three terms)

(v)

2y –(7/3) z ÷ x = 2y – (7z/3x) – It is binomial

(∵ It has two terms)

(vi)

3p x q ÷ z – (3pq/z) – It is monomial

(∵ It has one terms)

(vii)

12z ÷ 5x + 4 = (12z/5x)+4 – It is binomial

(∵ It has two terms)

(viii)

12 – 5 z – 4 = 8 – 5 z – It is binomial

(∵ It has two terms)

(ix)

a3 – 3ab2 x c  = a3 – 3ab2c  – It is binomial

(∵ It has two terms)

Question 3.

Write the coefficient of:
(i) xy in – 3axy
(ii) z2 in p2yz2
(iii) mn in -mn
(iv) 15 in – 15p2
Answer
(i) Co-efficient of xy in – 3 axy = – 3a

(ii) Co-efficient of z2 in p2yz2 = p2y

(iii) Co-efficient of mn in – mn = – 1

(iv) Co-efficient of 15 in – 15p2 is -p2

Question 4.

For each of the following monomials, write its degree :
(i) 7y
(ii) – x2y
(iii) xy2z
(iv) – 9y2z3
(v) 3 m3n4
(vi) – 2p2q3r4
Answer

(i) Degree of 7y = 1

(ii) Degree of – x2y = 2 + 1 = 3 

(iii) Degree of xy2z = 1 + 2 + 1 = 4 

(iv) Degree of – 9y2z3 = 2 + 3 = 5 

(v) Degree of 3m3n4 = 3 + 4 = 7 

(vi) Degree of – 2p2q3r4 = 2 + 3 + 4 = 9 

Question 5.

Write the degree of each of the following polynomials :
(i) 3y3-x2y2 + 4x
(ii) p3q2 – 6p2q5 + p4q4
(iii) – 8mn6+ 5m3n
(iv) 7 – 3x2y + y2
(v) 3x – 15
(vi) 2y2z + 9yz3
Answer
(i) The degree of 3y3 – x2y2+ 4x is 4 as x2 

(ii) The degree of p3q2 – 6p2q5 – p4q4 is 8 as p4 q4 is the term which has highest degree. 

(iii) The degree of – 8mn6 + 5m3n is 7 as – 8mx6 is the term that has the highest degree.

(iv) The degree of 7 – 3x2y + y2 is 3 as – 3x2y is the term which has the highest degree. 

(v) The degree of 3x – 15 is 1 as 3x is the term which is highest degree.

(vi) The degree of 2y2z + 9yz3 is 4 as 9yz3 has the highest degree. 

Question 6.

Group the like term together :
(i) 9x2, xy, – 3x2, x2 and – 2xy
(ii) ab, – a2b, – 3ab, 5a2b and – 8a2b
(iii) 7p, 8pq, – 5pq – 2p and 3p
Answer

(i) 9x2, – 3x2 and x2 are like terms xy and – 2xy are like terms.

(ii)

ab, – 3ab, are like terms,

– a2b, 5a2b, – 8a2b are like terms

(iii)

7p, – 2p and 3p are like terms,

8pq, – 5pq are like terms.

Question 7.

Write numerical co-efficient of each of the followings :
(i) y
(ii) -y
(iii) 2x2y
(iv) – 8xy3
(v) 3py2
(vi) – 9a2b3
Answer

(i) Co-efficient of y = 1

(ii) Co-efficient of-y = – 1

(iii) Co-efficient of 2x2y is = 2 

(iv) Co-efficient of – 8xy3 is = – 8 

(v) Co-efficient of 3py2 is = 3 

(vi) Co-efficient of – 9a2b3 is = – 9 

Question 8.

In -5x3y2z4; write the coefficient of:
(i) z2
(ii) y2
(iii) yz2
(iv) x3y
(v) -xy2
(vi) -5xy2z
Also, write the degree of the given algebraic expression.
Answer

(i)

-5x3y2z4

Co-efficient of z2 is -5x3y2z2

Degree of the given expression is 3 + 2 + 4 = 9

(ii)

-5x3y2z4

Co-efficient of y2 is -5x3z4

Degree of the given expression is 3 + 2 + 4 = 9

(iii)

-5x3y2z4

Co-efficient of yz2 is -5x3yz2

Degree of the given expression is 3 + 2 + 4 = 9

(iv)

-5x3y2z4

Co-efficient of x3y is -5yz4

Degree of the given expression is 3 + 2 + 4 = 9

(v)

-5x3y2z4

Co-efficient of -xy2 is 5x2z4

Degree of the given expression is 3 + 2 + 4 = 9

(vi)

-5x3y2z4

Co-efficient of -5xy2z is x2z3

Degree of the given expression is 3 + 2 + 4 = 9


Fundamental Concepts ICSE Class-7 Exe-11 B

Question 1.

Fill in the blanks :
(i) 8x + 5x = ………
(ii) 8x – 5x =……..
(iii) 6xy2 + 9xy2 =……..
(iv) 6xy2 – 9xy2 = ………
(v) The sum of 8a, 6a and 5b = ……..
(vi) The addition of 5, 7xy, 6 and 3xy = …………
(vii) 4a + 3b – 7a + 4b = ……….
(viii) – 15x + 13x + 8 = ………
(ix) 6x2y + 13xy2 – 4x2y + 2xy2 = ……..
(x) 16x2 – 9x2 = and 25xy2 – 17xy2=………

Answer

(i) 8x + 5x = 13x 

(ii) 8x – 5x = 3x 

(iii) 6xy2 + 9xy2 = 15xy2 

(iv) 6xy2 – 9xy2 = -3xy2 

(v) 

The sum of 8a, 6a and 5b

= 8a + 6a + 5b = 14a + 5b

(vi)

The addition of 5, 7xy, 6 and 3xy

= 5 + 6 + 7xy + 3xy = 11 + 10 xy

(vii)

4a + 3b – 7a + 4b

= 4a – 7a + 3b + 4b = -3a + 7b = 7b – 3a

(viii) – 15x + 13x + 8 = – 2x + 8 = 8 – 2x

(ix)

6x2y + 13xy2 – 4x2y + 2xy2

= 6x2y – 4x2y + 13xy2 + 2xy2 = 2x2y + 15xy2

(x) 16x2 – 9x2 =  7xand 25xy2 – 17xy2 = 8xy2 

Question 2.

Add :
(i)- 9x, 3x and 4x
(ii) 23y2, 8y2 and – 12y2
(iii) 18pq – 15pq and 3pq

Answer

(i)

– 9x, 3x and 4x

= – 9x + 7x = – 2x

(ii)

23y2 , 8y2 and – 12y2

= 31y2 – 12y2 = 19y2

(iii)

18pq – 15pq and 3pq

= 18pq + 3pq – 15pq = 21pq – 15pq = 6 pq

Question 3.

Simplify :
(i) 3m + 12m – 5m
(ii) 7n2 – 9n2 + 3n2
(iii) 25zy—8zy—6zy
(iv) -5ax2 + 7ax2 – 12ax2
(v) – 16am + 4mx + 4am – 15mx + 5am
Answer

(i)

3m + 12m – 5m

= 15m – 5m = 10m

(ii)

7n2 – 9n2 + 3n2

= 7n2 + 3n2 – 9n2

= 10n2 – 9n2 = n2

(iii)

25zy – 8zy  – 6zy

= 25zy – 14zy = 11zy

(iv)

-5ax2 + 7ax2 – 12ax2

= – 5ax2 – 12ax2 + 7ax2

= – 17ax2 + 7ax2 = – 10ax2 

(v)

– 16am + 4mx + 4am – 15mx + 5am

= – 16am + 4am + 5am + 4mx – 15mx

= – 16am + 9am + 4mx – 15mx

= – 7 am – 11 mx

Question 4.

Add :
(i) a + i and 2a + 3b
(ii) 2x + y and 3x – 4y
(iii)- 3a + 2b and 3a + b
(iv) 4 + x, 5 – 2x and 6x
Answer

(i)

a + b and 2a + 3b

=  a + b + 2a + 3b

= a + 2a + b + 3b = 3a + 4b

(ii)

2x + y and 3x – 4y

= 2x + 3x + y – 4y

= 5x – 3y

(iii)

– 3a + 2b and 3a + b

= – 3a + 3a + 2b + b

= 0 + 3b = 3b

(iv)

4 + x, 5 – 2x and 6x

= x – 2x + 6x + 4 + 5

= 7x – 2x + 9

= 5x + 9

Question 5.

Find the sum of:
(i) 3x + 8y + 7z, 6y + 4z- 2x and 3y – 4x + 6z
(ii) 3a + 5b + 2c, 2a + 3b-c and a + b + c.
(iii) 4x2+ 8xy – 2y2 and 8xy – 5y2 + x2
(iv) 9x2 – 6x + 7, 5 – 4x and 6 – 3x2
(v) 5x2 – 2xy + 3y2 and – 2x2 + 5xy + 9y2
and 3x2 -xy- 4y2
(vi) a2 + b2 + 2ab, 2b2 + c2 + 2bc
and 4c2-a2 + 2ac
(vii) 9ax – 6bx + 8, 4ax + 8bx – 7
and – 6ax – 46x – 3
(viii) abc + 2 ba + 3 ac, 4ca – 4ab + 2 bca
and 2ab – 3abc – 6ac
(ix) 4a2 + 5b2 – 6ab, 3ab, 6a2 – 2b2
and 4b2 – 5 ab
(x) x2 + x – 2, 2x – 3x2 + 5 and 2x2 – 5x + 7
(xi) 4x3 + 2x2 – x + 1, 2x3 – 5x2– 3x + 6, x2 + 8 and 5x3 – 7x
Answer

(i)

3x + 8y + 7z; 6y + 4z- 2x and 3y – 4x + 6z

3x + 8y + 7z + 6y + 4z – 2x + 3y – 4x + 6z

= 3x – 6x + 17y + 17z

= – 3x + 17y + 17z

(ii)

3a + 5b + 2c, 2a + 3b-c and a + b + c.

3a + 5b + 2c + 2a + 3b – c + a + b + c.

= 6a + 9b + 3c – c

= 6a + 9b + 2c

(iii)

4x2+ 8xy – 2y2 and 8xy – 5y2 + x2

4x2+ 8xy – 2y2 + 8xy – 5y2 + x2

= 4x2 + x2 + 8xy + 8xy – 2y2 – 5y2

= 5x2 + 16xy – 7y2

(iv)

9x2 – 6x + 7, 5 – 4x and 6 – 3x2

9x2 – 6x + 7 + 5 – 4x + 6 – 3x2

= 9x2 – 3x2 – 6x – 4x + 7 + 5 + 6

= 6x2 – 10x + 18

(v)

5x2 – 2xy + 3y2 and – 2x2 + 5xy + 9y2 and 3x2 -xy- 4y2

5x2 – 2xy + 3y2 + – 2x2 + 5xy + 9y2 + 3x2 -xy- 4y2

= 5x2 – 2x2 + 3x2 – 2xy + 5xy – xy + 3y2 + 9y2 – 4y2

= 8x2 – 2x2 + 5xy – 3xy + 12y2 – 4y2

=6x2 + 2xy + 8y2

(vi)

a2 + b2 + 2ab, 2b2 + c2 + 2bc and 4c2 -a2 + 2ac

a2 + b2 + 2ab + 2b2 + c2 + 2bc + 4c2 -a2 + 2ac

= a2 – a2 + b2 + 2b2 + c2 + 4c2 + 2ab + 2bc + 2ac

= 3b2 + 5c2 + 2ab + 2bc + 2ac

(vii)

9ax – 6bx + 8, 4ax + 8bx – 7 and – 6ax – 46x – 3

9ax – 6bx + 8 + 4ax + 8bx – 7  – 6ax – 46x – 3

= 9ax + 4ax – 6ax – 6bx + 8bx – 4bx + 8 – 7 – 3

= 13ax – 6ax + 8bx – 10bx + 8 – 10

= 7ax – 2bx – 2

(viii)

abc + 2 ba + 3 ac, 4ca – 4ab + 2 bca and 2ab – 3abc – 6ac

abc + 2 ba + 3 ac + 4ca – 4ab + 2 bca + 2ab – 3abc – 6ac

= abc + 2abc – 3abc + 2ab – 4ab + 2ab + 3ca + 4ca – 6ca

= 3abc – 3abc + 4ab – 4ab + 7ca – 6ca

= 0 + 0 + ca = ca

(ix)

4a2 + 5b2 – 6ab, 3ab, 6a2 – 2b2 and 4b2 – 5 ab

4a2 + 5b2 – 6ab + 3ab, 6a2 – 2b2 + 4b2 – 5 ab

= 4a2 + 6a2 + 5b2 – 2b2 + 4b2 – 6ab + 3ab – 5ab

= 10a2 + 9b2 – 2b2 – 11ab + 3ab

= 10a2 + 7b2 – 8ab

(x)

x2 + x – 2, 2x – 3x2 + 5 and 2x2 – 5x + 7

= x2 + x – 2 + 2x – 3x2 + 5 + 2x2 – 5x + 7

= x2 – 3x2 + 2x2 + x + 2x – 5x – 2 + 5 + 7

= 3x2 – 3x2 + 3x – 5x – 2 + 12

= 0 – 2x + 10

= – 2x + 10

(xi)

4x3 + 2x2 – x + 1, 2x3 – 5x2 – 3x + 6, x2 + 8 and 5x3 – 7x

4x3 + 2x2 – x + 1 + 2x3 – 5x2 – 3x + 6 + x2 + 8 + 5x3 – 7x

= 4x3 + 2x3 + 5x3 + 2x2 – 5x2 + x2 – x – 3x – 7x + 1 + 6 + 8

= 11x3 + 3x2 – 5x2 – 11x + 15

= 11x3 – 2x2 – 11x + 15

Question 6.

Find the sum of:
(i) x and 3y
(ii) -2a and +5
(iii) – 4xand +7x
(iv) +4a and -7b
(v) x3+3x2y and 2y2
(vi) 11 and -by
Answer

(i) x + 3y

(ii) -2a + 5

(iii) – 4x2 + 7x

(iv) + 4a and -7b = 4a – 7b

(v) x3+3x2y and 2y2 = x3+ 3x2y + 2y2 

(vi) 11 and -by = 11 – by

Question 7.

The sides of a triangle are 2x + 3y, x + 5y and 7x – 2y, find its perimeter.
Answer

Sides of a triangle are 2x + 3y, x + 5y, 7x – 2y

∴ Perimeter = sum of three sides of the triangle

= 2x + 3y + x + 5y + 7x – 2y

= 2x + x + 7x + 3y + 5y – 2y

= 10x + 8y – 2x

= 10x + 6y

Question 8.

The two adjacent sides of a rectangle are 6a + 96 and 8a – 46. Find its, perimeter.
Answer

Sides of a rectangle are 6a + 9b

and 8a – 4b

Let, length = 6a + 9b

and breadth = 8a – 4b

∴ Perimeter = 2 (l + b)

= 2 (6a + 9b + 8a – 4b)

= 2 (14 a + 5 b)

= 28a + 10b

Question 9.

Subtract the second expression from the first:

(i) 2a + b, a + b

(ii) – 2b + 2c, b + 3c

(iii) 5a + b, – 6b + 2a

(iv) a3 – 1 + a, 3a – 2a

(v) p + 2, 1

(vi) x + 2y + z, – x – y – 3z

(vii) 3a2 – 8ab – 2b2 , 3a2 – 4ab + 6b2

(viii) 4pq – 6p2 – 2q2 , 9p2

(ix) 10abc, 2a2 + 2abc – 4b2

(x) a2 + ab + c2, a2 – d2

Answer

(i)

(2a + b) – (a + b)

= 2a + b – a – b

= 2a – a + b – b

= a + 0 = a

(ii)

(- 2b + 2c) + (b + 3c)

= – 2b + 2c – b – 3c

= – 2b – b + 2c – 3c

= – 3b – c

(iii)

(5a + b) – (- 6b + 2a)

= 5a + b + 6b – 2a

= 5a – 2a + b + 6b

= 3a + 7b

(iv)

(a3 – 1 + a) – (3a – 2a2)

= a3 – 1 + a – 3a + 2a2

= a3 + 2a2 – 2a – 1

(v) (p + 2) – 1 = p + 2 – 1 = p + 1

(vi)

(x + 2y + z) – (- x – y – 3z)

= x + 2y + z + x + y+ 3z

= x + x + 2y + y + z + 3z

= 2x + 3y + 4z

(vii)

(3a2 – 8ab – 2b2) – (3a2 – 4ab + 6b2 )

= 3a2 – 8ab – 2b2 – 3a2 + 4ab – 6b2

= 3a2 – 3a2 – 2b2 – 6b2 – 8ab + 4ab

= 0 – 8b2 – 4ab

= – 4ab – 8b2

(viii)

(4pq – 6p2 – 2q2) – (9p2)

= 4pq – 6p2 – 2q2 – 9p2 

= 4pq – 15p2 – 2q2

(ix)

10abc – (2a2 + 2abc – 4b2 )

= 10 abc – 2a2 – 2abc + 4b2

= 10 abc – 2 abc – 2a2 + 4b2

= 8abc – 2a2 + 4b2

(x)

(a2 + ab + c2) – (a2 – d2 )

= a2 + ab + c2 – a2 + d2

= a2 – a2 + ab + c2 + d2

= ab + c2 + d2

Question 10.

Subtract:

(i) 4x from 8 – x

(ii) – 8c from c + 3d

(iii) – 5a – 2b from b + 6c

(iv) 4p + p2 from 3p2 – 8p

(v) 5a – 3b + 2c from 4a – b – 2c

(vi) – xy + yz – zx from xy – yz – xz

(vii)  2x2 – 7xy – y2 from 3x2 – 5xy + 3y2

(viii)  a2 – 3ab – 6b2 from 2b2 – a2 + 2ab

(ix) 4x2 – 5x2y + y2 from – 3y2 + 5xy2 – 7x2 – 9x2y

(x) 6m3 + 4m2 + 7m – 3 from 3m3 + 4

Answer

(i)

4x from 8 – x

= (8 – x) – 4x

= 8 – x – 4x

= 8 – 5x

(ii)

– 8c from c + 3d

= (c + 3d) – (- 8c)

= c + 3d + 8c

= 9c + 3d

(iii)

– 5a – 2b from b + 6c

= (b + 6c) – (- 5a – 2b)

= b + 6c + 5a + 2b

= 5a + 3b + 6c

(iv)

4p + p2 from 3p2 – 8p

= (3p2 – 8p) – (4p + p2)

= 3p2 – 8p – 4p – p2

= 2p2 – 12p

(v)

5a – 3b + 2c from 4a – b – 2c

= (4a – b – 2c) – (5a – 3b + 2c)

= 4a – b – 2c – 5a + 3b – 2c

= 4a – 5a – b + 3b – 2c – 2c

= – a + 2b – 4c

(vi)

– xy + yz – zx from xy – yz – xz

= (xy – yz – xz) – (- xy + yz – xz)

= xy – yz + zx + xy – yz + xz

= xy + xy – yz – yz + zx + xz

= xy + xy – yz – yz + zx + xz

= 2(xy – yz + zx)

(vii)

2x2 – 7xy – y2 from 3x2 – 5xy + 3y2

= (3x2 – 5xy + 3y2) – (2x2 – 7xy – y2)

= 3x2 – 5xy + 3y2 – 2x2 + 7xy + y2

= 3x2 – 2x2 – 5xy + 7xy + 3y2 + y2

= x2 + 2xy + 4y2

(viii)

a2 – 3ab – 6b2 from 2b2 – a2 + 2ab

= (2b2 – a2 + 2ab) – (a2 – 3ab – 6b2)

= 2b2 – a2 + 2ab – a2 + 3ab + 6b2

= – a2 + a2 + 2b2 + 6b2 + 2ab + 3ab

= – 2a2 + 8b2 + 5ab

= 8b2 + 5ab – 2a2

(ix)

4x2 – 5x2y + y2 from – 3y2 + 5xy2 – 7x2 – 9x2y

= (- 3y2 + 5xy2 – 7x2 – 9x2y) – (4x2 – 5x2y + y2)

= – 3y2 + 5xy2 – 7x2 – 9x2y – 4x2 + 5x2y  – y2

= – 3y– y2 + 5xy2 – 7×2 – 4x2 – 9x2y + 5x2y

= – 4y2 + 5xy2 – 11x2 – 4x2y

(x)

6m3 + 4m2 + 7m – 3 from 3m3 + 4

= (3m3 + 4) – (6m3 + 4m2 + 7m – 3)

= 3m3 + 4 – 6m3 + 4m2 + 7m – 3

= 3m– 6m3 – 4m2 – 7m + 4 + 3

= – 3m3 – 4m2 – 7m + 7

Question 11.

Subtract – 5a2 – 3a + 1 from the sum of 4a2 + 3 – 8a and 9a – 7.
Answer

sum of 4a2 + 3 – 8a and 9a – 7

= 4a2 + 3 – 8a + 9a – 7 = 4a2 + a – 4

∴ (4a2 + a – 4) – (- 5a2 – 3a + 1)

= 4a2  + a – 4 + 5a2 + 3a – 1

= 4a2 + 5a2 + a + 3a – 4 – 1

= 9a2 + 4a – 5

Question 12.

By how much does 8x3 – 6x2 + 9x – 10 exceed 4x3 + 2x2 + 7x -3 ?
Answer

8x3 – 6x2 + 9x – 10 exceeds 4x3 + 2x2 + 7x -3

= (8x3 – 6x2 + 9x – 10) – (4x3 + 2x2 + 7x – 3)

= 8x3 – 6x2 + 9x – 10 – 4x3 + 2x2 + 7x – 3

= 8x– 4x3 – 6x2 – 2x2 + 9x – 7x – 10 + 3

= 4x3 – 8x2 + 2x – 7

Question 13.

What must be added to 2a3 + 5a – a2 – 6 to get a2 – a – a3 + 1 ?
Answer

We get, the required result by subtracting

2a3 + 5a – a2 – 6 from – a3 + a2 – a + 1

= (- a3 + a2 – a + 1) – (2a3  – a2 + 5a – 6)

= – a3 + a2 – a + 1 – 2a3  + a2 – 5a + 6

= – a – 2a3 + a2 + a– a – 5a + 1 + 6

= – 3a3 + 2a2 – 6a + 7

Question 14.

What must be subtracted from a2 + b2 + lab to get – 4ab + 2b2 ?
Answer

We get, the required result by subtracting

– 4ab + 2b2 from a2 + b2 + 2ab

= a2 + b2 + 2ab – (- 4ab + 2b2)

= a2 + b2 + 2ab + 4ab – 2b2

= a2 + b– 2b2 + 2ab + 4ab

= a2 – b2 + 6ab

Question 15.

Find the excess of 4m2 + 4n2 + 4pover m2+ 3n2 – 5p2
Answer

The required result will be by substracting

m2+ 3n2 – 5pfrom  4m2 + 4n2 + 4p2

= 4m2 + 4n2 + 4p2 – (m2 + 3n2 – 5p2)

= 4m2 + 4n2 + 4p2 – m2 – 3n2 – 5p2

= 4m2 – m2 + 4n2 – 3n2 + 4p2 + 5p2

= 3m2 + n2 + 9p2 

Question 16.

By how much is 3x3 – 2x2y + xy2 -y3 less than 4x3 – 3x2y – 7xy2 +2y3
Answer

We can get the required results by substracting

3x– 2x2y + xy2 -y3 from 4x3 – 3x2y – 7xy2 +2y3

= (4x3 – 3x2y – 7xy2 +2y3 ) – (3x– 2x2y + xy2 -y3)

= 4x3 – 3x2y – 7xy2 +2y3 – 3x3 + 2x2y – xy2 + y

= 4x– 3x3 – 3x2y + 2x2y – 7xy2 – xy2 +2y3 + y

= x3 – x2y – 8xy2 + 3y3

Question 17.

Subtract the sum of 3a2 – 2a + 5 and a2 – 5a – 7 from the sum of 5a2 -9a + 3 and 2a – a2 – 1
Answer

Sum of 3a2 – 2a + 5 and a2 – 5a – 7

= 3a2 – 2a + 5 + a2 – 5a – 7

= 3a2 + a2 – 2a – 5a + 5 – 7

= 4a2 – 7a – 2

and sum of 5a2 -9a + 3 and 2a – a2 – 1

= 5a2 – 9a + 3 + 2a – a2 – 1

= 5a2 – a2 – 9a + 2a + 3 – 1

= 4a2 – 7a + 2

Now (4a2 – 7a + 2) – (4a2 – 7a – 2)

= 4a2 – 7a + 2 – 4a2 + 7a + 2

= 4a2 – 4a2  – 7a + 7a + 2 + 2

= 0 + 0 + 4 = 4

Question 18.

The perimeter of a rectangle is 28x3+ 16x2 + 8x + 4. One of its sides is 8x2 + 4x. Find the other side
Answer

Perimeter of a rectangle (2l + 2b)

= 28x3 + 16x2 + 8x + 4

Let one side (l) = 8x2 + 4x

∴ 2l = 2 (8x2 + 4x) = 16x2 + 8x

∴ 2b = (28x3 + 16x2 + 8x + 4) – (16x2 + 8x)

= 28x3 + 16x2 + 8x + 4 – 16x2 – 8x

= 28x3 + 4

∴ Other side (b) = (28x3+4)/2

=14×3+2

Question 19.

The perimeter of a triangle is 14a2 + 20a + 13. Two of its sides are 3a2 + 5a + 1 and a2 + 10a – 6. Find its third side.
Answer

perimeter of a triangle = 14a2 + 20a + 13

Sum of two sides

= 3a2 + 5a + 1 + a2 + 10a – 6

= 3a2 + a2 + 5a + 10a + 1 – 6

= 4a2 + 15a – 5

∴ Third side = (14a2 + 20a + 13) – (4a2 + 15a – 5)

= 14a2 + 20a + 13 – 4a2 – 15a + 5

= 14a2 – 4a2 + 20a – 15a + 13 + 5

= 10a2 + 5a + 18

Question 20.

(i) If x = 4a2 + b2 – 6ab; y = 3b2 – 2a2 + 8ab and z = 6a2 + 8b2 – 6ab

find: x + y + z

(ii) If x = 4a2 + b2 – 6ab; y = 3b2 – 2a2 + 8ab and z = 6a2 + 8b2 – 6ab

find: x – y – z
Answer

(i)

x = 4a2 + b2 – 6ab
y = 3b2 – 2a2 + 8ab
z = 6a2 + 8b2 – 6ab

x + y + z

= 4a2 + b2 – 6ab + 3b2 – 2a2 + 8ab + 6a2 + 8b2 – 6ab

= 4a2 – 2a2 + 6a2 + b2 + 3b2 + 8b2 – 6ab + 8ab – 6ab

= 10a2 – 2a2 + 12b2 – 12ab + 8ab

= 8a2 + 12b2 – 4ab

(ii)

x = 4a2 + b2 – 6ab
y = 3b2 – 2a2 + 8ab
z = 6a2 + 8b2 – 6ab

x – y – z

= (4a2 + b2 – 6ab) – (3b2 – 2a2 + 8ab) – (6a2 + 8b2 – 6ab)

= 4a2 + b2 – 6ab – 3b2 + 2a2 – 8ab – 6a2 – 8b2 + 6ab

= 4a2 – 2a2 – 6a2 + b2 – 3b2 – 8b2 – 6ab – 8ab + 6ab

= 6a2 – 6a2 + b2 – 11b2 – 14ab + 6ab

= – 10b2 – 8ab

Question 21.

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-b21
Answer

(i)

m = 9x2 – 4xy + 5y2

n = – 3x2 + 2xy – y2

∴ 2m – n

= 2 (9x2 – 4xy + 5y2) – (- 3x2 + 2xy – y2)

= 18x2 – 8xy + 10y2 + 3x2 – 2xy + y2

= 18x2 + 3x2 – 8xy – 2xy + 10y2 + y

= 21x2 – 10xy + 11y2

(ii)

m = 9x2 – 4xy + 5y2

n = – 3x2 + 2xy – y2

∴ m + 2n

= (9x2 – 4xy + 5y2) + 2 (- 3x2 + 2xy – y2)

= 9x2 – 4xy + 5y2 – 6x2 + 4xy – 2y2

= 9x2 – 6x2 – 4xy + 4xy + 5y2 – 2y2

= 3x2 + 3y2

(iii)

m = 9x2 – 4xy + 5y2

n = – 3x2 + 2xy – y2

∴ m – 3n

= (9x2 – 4xy + 5y2) – 3 (- 3x2 + 2xy – y2)

= 9x2 – 4xy + 5y2 + 9x2 – 6xy + 3y2

= 18x2 – 10xy + 8y2

Question 22.

Simplify:
Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-b22
Answer

(i)

3x + 5(2x + 6) – 7x

⇒ 3x + 10x + 30 – 7x

⇒ 3x + 10x – 7x + 30

⇒ 13x – 7x + 30

⇒ 6x + 30

(ii)

3(4y – 10)  2(y – 1)

⇒ 12y – 30 + 2y – 2

⇒ 12y + 2y – 30 – 2

⇒ 14y – 32

(iii)

– (7 + 6x) – 7(x + 2)

⇒ – 7 – 6x – 7x – 14

⇒ – 7x – 6x – 7 – 14

⇒  -13 x – 21

(iv)

x – (x – y) – y – (y – x)

⇒ x – x + y – y – y + x

⇒ 2x – x – 2y + y

⇒ x – y

(v)

4x + 7y – (5y – 8) – 2x

⇒ 4x + 7y – 5y + 8 – 2x

⇒ 4x – 2x + 7y – 5y + 8

⇒ 2x + 2y + 8

(vi)

– 2m + 5 + 4(m – 3)

⇒ – 2m + 5 + 4m – 12

⇒ – 2m + 4m + 5 – 12

⇒ 2m – 7

(vii)

2x – y + 5 – (x – y)

⇒ 2x – y + 5 – (x – y)

⇒ 2x – x + 5

⇒ x + 5

(viii)

2(x – y) – (x – 8)

⇒ 2x – 2y – x + 8

⇒ 2x – x – 2y + 8

⇒ x – 2y + 8

(ix)

4(3x – 8) – 3(5x + 3) – 2(6x – 8)

⇒ 12x – 32 – 15x – 9 – 12x + 16

⇒ 12x – 15x – 12x – 32 – 9 + 16

⇒ 12x – 27x – 41 + 16

⇒ – 15 x – 25

(x)

5(x – 4) – 3(x – 4) + 7(x – 4)

⇒ 5x – 20 – 3x + 12 + 7x – 28

⇒ 5x + 7x – 3x + 12 + 7x – 28

⇒ 12x – 3x – 48 + 12

⇒ 9x – 36

 


Exe – 11 C Soved Questions of Fundamental Concepts for ICSE Class-7 

Question 1.

Multiply:
Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-c1
Answer

(i)

Product of 3x, 5x2y and 2y

= 3x + 5x2y × 2y

= 3 × 5 × 2 × x × x2 × y × y

= 30x3y2

(ii)

Product of 5, 3a and 2ab2

= 5 × 3a × 2ab2

= 5 × 3 × 2 × a × ab2

= 30a2b2

(iii)

Product of 5x + 2y and 3xy

= 3xy (5x + 2y)

= 3xy × 5x + 3xy × 2y

= 15x2y + 6xy2

(iv)

Product of 6a – 5b and – 2a

= -2a (6a – 5b)

= – 2a × 6a + (- 2a) × (- 5b)

= – 12a2 + 10ab

(v)

Product of 4a + 5b and 4a – 5b

= 16a2 – 25b2

4a + 5b

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 1

(vi)

Product of 9xy + 2y2 and 2x – 3y

= 18x2y – 23xy2 – 6y3

9xy + 2y2

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 2

(vii)

Product of – 3m2n + 5mn – 4mn2 and 6m2n

= 6m2n (- 3m2n + 5mn – 4mn2 )

= 6m2n × (- 3m2n) + 6m2n × 5mn + 6m2n ×  (- 4mn2)

= 18m4n2 + 30m3n2 – 24 m3n3

(viii)

Product of 6xy2 – 7x2y2 + 10x3 and – 3x2y3

= – 3x2y3 (6xy2 – 7x2y2 + 10x3)

= – 3x2y3  × 6xy2  + (- 3x2y3) × (- 7x2y2 ) + (- 3x2y3) × 10x3

= – 18x3y5 + 21x4y5 – 30x5y3

Question 2.

Copy and complete the following multi-plications :
Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-c2

Answer

(i) 

3a + 2b
× – 3xy
– 9axy – 6bxy  

(ii) 

9x + 5y
× – 3xy
– 27x2y + 15xy2 

(iii) 

3xy – 2x2 – 6x
×     -5x2y
-15x3y2 + 10x4y + 30x3y

(iv) 

a + b
× a + b
a2 + ab
ab + b
a2 + 2ab + b2 

(v) 

ax – b
× 2ax + 2b2
2a2x2 – 2abx + 2ab2x – 2b3 

(vi) 

2a – b + 3c
× 2a – 4b
4a2 – 2ab + 6ac
– 8ab + 4b2 – 12bc
4a2 – 10ab + 6ac + 4b2 – 12bc

(vii) 

3m2 + 6m – 2n
× 5n – 3m
15m2n + 30mn – 10n2 – 9m3 – 18m2
+ 6mn
15m2n + 36mn – 10n2 – 9m3 – 18m2

(viii)

6 – 3x + 2x2
× 1 + 5x – x2
6 – 3x + 2x2
+ 30x – 15x2 + 10x3
– 6x2 + 3x3 – 2x4
6 + 27x – 19x2 + 13x3 – 2x 

(ix) 

4x3 – 10x2 + 6x – 8
× 3 + 2x – x2
12x3 – 30x2 + 18x – 24
8x4 – 20x3 + 12x2 – 16x
4x5 + 10x4 – 6x3 + 8x
4x5 + 18x4 – 14x3 – 10x2 + 2x – 24  

Question 3.

Evaluate :
Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-c3
Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-c3..

Answer

(i)

(c + 5)(c – 3) = c (c – 3) +5 (c – 3)

= c2 – 3c + 5c – 15

= c2 + 2c – 15

(ii)

(3c – 5d)(4c – 6d)

= 3c (4c – 6d) – 5d(4c – 6d)

= 12c2 – 18cd – 20cd + 30d2

= 12c2 – 38cd + 30d2

(iii) 

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 3

(iv)

(a2 + 2ab + b2)(a + b)

= a(a2 + 2ab + b2) + b(a2 + 2ab + b2)

= a3 + 2a2b + ab2 + a2b + 2ab2 + b3

= a3 + 3a2b + 3ab2 + b3

(v)

(3x – 1)(4x3 – 2x2 + 6x – 3)

= 3x (4x3 – 2x2 + 6x – 3) – 1 (4x3 – 2x2 + 6x – 3)

= 12x4 – 6x3 + 18x2 – 9x – 4x3 + 2x2 – 6x + 3

= 12x4 – 6x3 – 4x3 + 18x2 + 2x2 – 9x – 6x + 3

= 12x4 – 10x3 + 20x2 – 15x + 3

(vi)

(4m – 2)(m2 + 5m – 6)

= 4m (m2 + 5m – 6) – 2(m2 + 5m – 6)

= 4m3 + 20m2 – 24m – 2m2 – 10m + 12

= 4m3 + 20m2 – 2m2 – 24m – 10m + 12

= 4m3 + 18m2 – 34m + 12

(vii)

(8 – 12x + 7x2 – 6x3)(5 – 2x)

= 5(8 – 12x + 7x2 – 6x3) – 2x (8 – 12x + 7x2 – 6x3)

= 40 – 60x + 35x2 – 30x3 – 16x + 24x4 – 14x3 + 12x4

= 40 – 60x – 16x + 35x2 + 24x4 – 30x3 – 14x3 + 12x4

= 40 – 76x + 59x2 – 44x3 + 12x4 

(viii)

(4x2 – 4x + 1)(2x3 – 3x2 + 2)

= 4x2 (2x3 – 3x2 + 2) – 4x (2x3 – 3x2 + 2) + 1 (2x3 – 3x2 + 2)

= 8x5 – 12x4 + 8x2 – 8x4 + 12x3 – 8x + 2x3 – 3x2 + 2

= 8x5 – 12x4 – 8x4 + 12x3 + 2x3 + 8x2 – 3x2 – 8x  + 2

= 8x5 – 20x4 + 14x3 + 5x2 – 8x + 2

(ix)

(6p2 – 8pq + 2q2) (- 5p)

= -5p × 6p2 – 5p × (- 8pq) – 5p (2q2)

= – 30p3 + 40p2q – 10pq2

(x)

– 4y (15 + 12y – 8z) (x – 2y)

= – 4y (x – 2y)(15x + 12y – 8z)

= (- 4xy + 8y2)(15x + 12y – 8z)

= – 4xy (15x + 12y – 8z) + 8y2 (15x +12y – 8z)

= -60x2y – 48xy2 + 32xy + 120xy2 + 96y3 – 64y2z

= -60x2y – 48xy2 + 120xy2 – 64y2z + 96y3 + 32xy

= -60x2y + 72xy2 – 64y2z + 96y3 + 32xyz

(xi)

(a2 + b2 + c2 – ab – bc – ca)(a + b + c)

= a (a2 + b2 + c2 – ab – bc – ca) + b (a2 + b2 + c2 – ab – bc – ca) + c (a2 + b2 + c2 – ab – bc – ca)

= a3 + ab2 + ac2 – a2b – abc – ca2 +a2b + b3 + bc2 – ab2 – b2c  – abc + a2c + b2c + c3 – abc – bc2 – c2a

= a3 + b3 + c3 -a2b + a2b – ca2 + a2c + bc2 – bc2 – ab2 + ab2 – abc – abc – abc + ac2 – ac2 + b2c – b2c

= a3 + b3 + c3 – 3abc

Question 4.

Evaluate:
Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-c4

Answer

(i)

(a + b)(a – b)

= a (a – b) + b(a – b)

= a2 – ab + ab – b2

= a2 – b2

(ii) 

(a2 + b2)(a + b)(a – b)

= (a2 + b2)(a2 – b2)    …{from(i)}

= a2 (a2 – b2) + b2 (a2 – b2)

= a4 – a2b2 + a2b2 – b4

= a8 – a4b4 + a4b4 – b8

= a4 – b4

(iii) 

(a4 + b4)(a2 + b2)(a + b)(a – b)

= (a4 + b4) (a4 – b4)  ….{from(ii)}

= a4 (a4 + b4) + b4 (a4 + b4)

= a8 – a4b4 + a4b4 – b8

= a8 – b8

Question 5.

Evaluate :
Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-c5

Answer

(i)

(3x – 2y)(4x + 3y)

= 3x (4x + 3y) – 2y (4x + 3y)

= 12x2 + 9xy – 8xy – 6y2 

= 12x2 + xy – 6y2

(ii)

(3x – 2y)(4x + 3y)(8x – 5y)

= 3x (4x + 3y) – 2y (4x + 3y)(8x – 5y)

= (12x2 + 9xy – 8xy – 6y)(8x – 5y)

= (12x2 + xy – 6y2 )(8x – 5y)

= 8x (12x2 + xy – 6y2 ) – 5y (12x2 + xy – 6y2 )

= 96x3 + 8x2y – 48xy2 – 60x2y – 5xy2 + 30y3

= 96x3 + 8x2y – 60x2y – 48xy– 5xy2 + 30y3

= 96x3 – 52x2y – 53xy2 + 30y3

(iii)

(a + 5)(3a – 2)(5a + 1)

= {a (3a – 2) + 5(3a – 2)} (5a + 1)

= (3a2 – 2a + 15a – 10)(5a + 1)

= (3a2 + 13a – 10)(5a + 1)

= 5a (3a2 + 13a – 10) + 1 (3a2 + 13a – 10)

= 15a3 + 65a2 – 50a + 3a2 + 13a – 10

= 15a3 + 68a2 – 37a – 10

(iv)

(a + 1)(a2 – a + 1) and (a – 1)(a2 + a + 1)

= a (a2 – a + 1) + 1 (a2 – a + 1)

= a3 – a2 + a + a2 – a + 1

= a3 + 1

(a – 1)(a2 + a + 1)

= a(a2 + a + 1) – 1(a2 + a + 1)

= a3 + a2 + a – a2 – a – 1

= a3 – 1

Now, (a + 1)(a2 – a + 1) + (a – 1)(a2 + a + 1)

= a3 + 1 + a3 – 1

= 2a3

(v)

(5m – 2n)(5m + 2n)(25m2 + 4n2)

= {5m (5m + 2n) – 2n(5m + 2n)} (25m2 + 4n2)

= (25m2 + 10mn – 10mn – 4n2)(25m2 + 4n2)

= (25m2 – 4n2)(25m2 + 4n2)

= 25m2 (25m2 + 4n2) – 4n2 (25m2 + 4n2)

= 625m4 + 100m2n2 – 100m2n2 – 16n4

= 625m4 – 16n4

Question 6.

Multiply:
Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-c6
Answer

(i)

mn4, m3n and 5m2n3

⇒ 5m2n3 × mn4 × m3n

⇒5m2+1+3 n3+4+1

= 5m6n

(ii)

2mnpq, 4mnpq and 5mnpq

⇒ 5mnpq × 2mnpq  × 4mnpq

⇒5×2×4m1+1+1  n1+1+1  p1+1+1 q1+1+1

⇒ 40m3n3p3q3 

(iii)

pq – pm and p2m

⇒ p2m × (pq – pm)

⇒ p3qm – p3m2

(iv)

x3 – 3y3 and 4x2y2

⇒ 4x2y2 × (x3 – 3y3)

⇒ 4x5y2 – 12x2y5

(v)

a3 – 4ab and 2a2b

⇒ 2a2b × (a3 – 4ab)

⇒ 2a5b – 8a3b2

(vi)

x2 + 5yx – 3y2 and 2x2y

⇒ 2x2y × (x2 + 5yx – 3y2)

⇒ 2x4y + 10x3y2 – 6x2y3

Question 7.

Multiply:
Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-c7

Answer

(i)

(2x + 3y)(2x + 3y)

⇒ 2x (2x + 3y) + 3y(2x + 3y)

⇒ 4x2 + 6xy + 6xy + 9y

⇒ 4x2 + 12xy + 9y2

(ii)

(2x – 3y)(2x + 3y)

⇒ 2x (2x + 3y) – 3y(2x + 3y)

⇒ 2x × 2x + 2x × 3y – 3y × 2x – 3y × 3y

⇒ 4x2 + 6xy – 6xy – 9y2

⇒ 4x2 + 0 – 9y2

⇒ 4x2 – 9y2

(iii)

(2x – 3y)(2x + 3y)

⇒ 2x (2x + 3y) – 3y(2x + 3y)

⇒ 2x × 2x + 2x × 3y – 3y × 2x – 3y × 3y

⇒ 4x2 + 6xy – 6xy – 9y2

⇒ 4x2 + 0 – 9y2

⇒ 4x2 – 9y2

(iv)

(2x – 3y)(2x – 3y)

⇒ 2x (2x – 3y) – 3y(2x – 3y)

⇒ 2x × 2x – 2x × 3y + 3y × 2x + 3y × 3y

⇒ 4x2 – 6xy – 6xy + 9y2

⇒ 4x2 – 12xy + 9y2

(v)

(- 2x + 3y)(2x – 3y)

⇒ – 2x (2x – 3y) + 3y(2x – 3y)

⇒ – 4x2 + 6xy + 6xy – 9y2

⇒ – 4x2 + 12xy – 9y2

(vi)

(xy + 2b)(xy – 2b)

⇒ xy (xy – 2b) + 2b (xy – 2b)

⇒ x2y2 – 2bxy + 2bxy – 4b2

⇒ x2y2 – 4b2

(vii)

(x – a)(x + 3b)

⇒ x (x + 3b) – a (x + 3b)

⇒ x2 + 3bx – ax – 3ab

(viii)

(2x + 5y + 6)(3x + y – 8)

⇒ 2x (3x + y – 8) + 5y(3x + y – 8) + 6 (3x + y – 8)

⇒ 6x2 + 2xy – 16x + 15xy + 5y2 – 40y + 18x + 6y – 48

⇒ 6x2 + 2xy + 15xy – 16x + 18x + 5y2 – 40y + 6y – 48

⇒ 6x2 + 17xy + 2x + 5y2 – 34y – 48

(ix)

(3x – 5y + 2)(5x – 4y – 3)

⇒ 3x (5x – 4y – 3) – 5y (5x – 4y – 3) + 2 (5x – 4y – 3)

⇒ 15x2 – 12xy – 9x – 25xy + 20y2 + 15y + 10x – 8y – 6

⇒ 15x2 – 12xy – 25xy – 9x + 10x + 20y2 + 15y – 8y – 6

⇒ 15x2 – 37xy + x + 20y2 + 7y – 6

(x)

(6x – 2y)(3x – y)

⇒ 6x (3x – y) – 2y (3x – y)

⇒ 18x2 – 6xy – 6xy + 2y2

⇒ 18x2 – 12xy + 2y2

(xi)

(1 + 6x2 – 4x3)(-1 + 3x – 3x2)

⇒ 1(- 1 + 3x – 3x2) + 6x2 (- 1 + 3x – 3x2) – 4x3 (- 1 + 3x – 3x2)

⇒ – 1 + 3x – 3x2 – 6x2 + 18x3 – 18x4 + 4x3 – 12x4 + 12x5

⇒ – 1 + 3x – 9x2 + 22x3 – 30x4 + 12x5

 


 ICSE Class-7 Concise Selina mathematics Solutions Exe- 11 D 

Question 1.

Divide:
Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-d1
Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-d2

Answer

(i)

– 16ab2c by 6abc

=-16ab2c/6abc

=-(8/3)b

(ii)

25x2y by – 5y2

=25x2y/-5y2 

=-5x2 /y

(iii)

8x + 24 by 4

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 4

(iv)

4a2 – a by – a

= (4a2-a)/-a

= (4a2 /-a) – (a-a)

= – 4a + 1

(v)

8m – 16 by – 8

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 5

(vi) 

– 50 + 40p by 10p

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 6

(vii) 4x3 – 2x2 by – x 

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 7

 = – 4x2 + 2x

(viii)

10a3 – 15a2b by – 5a2

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 8

(ix) 12x3y – 8x2y2 + 4x2y3 by 4xy 

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 9

= 3x2 – 2xy + xy2 

(x) 9a4b – 15a3b2 + 12a2b3 by – 3a2

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 10

= – 3a2 + 5ab – 4b2 

Question 2.

Divide :
Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-d

Answer

(i)

9a4b – 15a3b2 + 12a2b3 by – 3a2b

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 11

= – 3a2 + 5ab – 4b2

(ii)

m2 – 2mn + n2 by m – n

m – n

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 12

= m – n

(iii)

a2 + 4a + 1 by 2a + 1

2a + 1

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 13

= 2a + 1

(iv)

p2 + 4p + 4 by p + 2

p + 2

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 14

= p + 2

(v)

x2 + 4xy + 4y2 by x + 2y

x + 2y

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 15

= x + 2y

(vi)

2a2 – 11a + 12 by a – 4

2a – 3

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 16

= 2a – 3

(vii)

6x2 + 5x – 6 by 2x + 3

3x – 2
Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 17

= 3x – 2

(viii)

8a2 + 4a – 60 by 2a – 5

4a + 12

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 18

= 4a + 12

(ix)

9x2 – 24xy + 16y2 by 3x- 4y

3x – 4y

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 19

= 3x – 4y

(x)

15x2 + 31xy + 14y2 by 5x + 7y

3x + 2y

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 20

= 3x + 2y

(xi)

35a3 + 3a2b – 2ab2 by 5a – b

7a2 + 2ab

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 21

= 7a2 + 2ab

(xii)

6x3 + 5x2 – 21x + 10 by 3x – 2

2x2 + 3x – 5

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 22

= 2x2 + 3x – 5

Question 3.

The area of a rectangle is 6x2– 4xy – 10y2 square unit and its length is 2x + 2y unit. Find its breadth
Answer

Area of a rectangle

= 6x2 – 4xy – 10y2 sq.units

Length = 2x + 2y units

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 23

= 3x – 5y units

Hence breadth = 3x – 5y units

Question 4.

The area of a rectangular field is 25x2 + 20xy + 3y2 square unit. If its length is 5x + 3y unit, find its breadth, Hence find its perimeter.
Answer

Area of a rectangle

= 25x2 + 20xy + 3y2

Length = (5x + 3y) units

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 24

Hence Breadth = 5x + y

Hence perimeter of rectangular field

= 2 (l + b)

= 2 (5x + 3y + 5x + y)

= 2 (10x + 4y)

= 20x + 8y

Question 5.

Divide:
Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-d5
Answer

(i)

2m3n5 by – mn

= 2m3n5 / -mn

= – 2m2n4

(ii) 5x2 – 3x by x

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 25

= 5x – 3

(iii) 10x3y – 9xy2 – 4x2y2 by xy 

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 26

= 10x2 – 9y – 4xy 

(iv)

3y3 – 9ay2 – 6ab2y by -3y

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 27

= – y2 + 3ay2 + 2ab2

(v)

x5 – 15x4 – 10x2 by -5x2

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 28

(vi) 12a2 + ax – 6x2 by 3a – 2x 

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 29

= 4a + 3x 

(vii)

6x2 – xy – 35y2 by 2x – 5y

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 30

= 3x + 7y

(viii) x3 – 6x2 + 11x – 6 by x2 – 4x + 3 

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 31

= x – 2 

(ix)

m3 – 4m2 + m + 6 by m2 – m – 2

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 32

= m – 3


Fundamental Concepts ICSE Class-7 Exe- 11 E

Simplify

Question 1.

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-e1
Answer

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 33

Question 2.

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-e2

Answer

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 34

Question 3.

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-e3
Answer

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 35

Question 4.

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-e4
Answer

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 36

Question 5.

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-e5
Answer

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 37

Question 6.

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-e6
Answer

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 38

Question 7.

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-e7
Answer

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-e7

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 39

(LCM of 2, 3, 5 = 30)

Question 8.

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-e8
Answer

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-e8

(LCM of 5, 4 = 20)

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 40

Question 9.

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-e9
Answer

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-e9

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 41

Question 10.

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-e10

Answer

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-e10

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 42

Question 11.

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-e11

Answer

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-e11

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 43

Question 12.

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-e12

Answer

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-e12

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 44

Question 13.

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-e13

Answer

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-e13

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 45

Question 14.

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-e14

Answer

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-e14

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 46

Question 15.

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-e15

Answer

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-e15

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 47

Question 16

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-e16

Answer

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-e16

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 48

Question 17.

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-e17

Answer

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-e17

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 49

Question 18.

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-e18

Answer

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-e18

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 50

.(LCM of 3,2 = 6)

Question 19.

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-e19

Answer

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-e19

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 51

Question 20.

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-e20

Answer

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-e20

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 52

Question 21

.
Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-e21

Answer

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-e21

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 53

Question 22.

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-e22

Answer

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-e22

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 54

Question 23.

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-e23

Answer

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-e23

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 55

Question 24.

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-e24

Answer

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-e24

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 56

Question 25.

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-e25

Answer

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-e25

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 57

Question 26.

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-e26

Answer

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-e26

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 58


Exe – 11 F Concise Selina Maths ICSE Class-7

Enclose the given terms in brackets as required :

Question 1.

x – y – z = x-{…….)
Answer

x – y – z = x – (y + z) 

Question 2.

x2 – xy2 – 2xy – y2 = x2 – (…….. )
Answer

x2 – xy2 – 2xy – y2

= x2 – (xy2 + 2xy + y2)

Question 3.

4a – 9 + 2b – 6 = 4a – (…….. )
Answer

4a – 9 + 2b – 6

= 4a – (9 – 2b + 6) 

Question 4.

x2 -y2 + z2 + 3x – 2y = x2 – (…….. )
Answer

x2 -y2 + z2 + 3x – 2y

= x2 – (y2 – z2 – 3x + 2y) 

Question 5.

– 2a2 + 4ab – 6a2b2 + 8ab2 = – 2a (……… )
Answer

– 2a2 + 4ab – 6a2b2 + 8ab2

= – 2a (a – 2b + 3ab2 – 4b2)

 

Simplify :

Question 6.

2x – (x + 2y- z)
Answer

2x – (x + 2y- z)

= 2x – x – 2y + z

= x – 2y + z

Question 7.

p + q – (p – q) + (2p – 3q)
Answer

p + q – (p – q) + (2p – 3q)

= p + q – p + q + 2p – 3q

= 2p – q

Question 8.

9x – (-4x + 5)
Answer

9x – (- 4x + 5)

= 9x + 4x – 5

= 13x – 5

Question 9.

6a – (- 5a – 8b) + (3a + b)
Answer

6a – (- 5a – 8b) + (3a + b)

= 6a + 5a + 8b + 3a + b

= 6a + 5a + 3a + 8b + b

= 14a + 9b

 Question 10.

(p – 2q) – (3q – r)
Answer

(p – 2q) – (3q – r)

=p – 2q – 3q + r

=p – 5q + r

Question 11.

9a (2b – 3a + 7c)
Answer

9a (2b – 3a + 7c)

= 18ab – 27a2 + 63ca

Question 12.

-5m (-2m + 3n – 7p)
Answer

– 5m (-2m + 3n – 7p)

= – 5m x (-2m) + (-5m) (3n) – (-5m) (7p)

= 10m2 – 15mn + 35 mp.

Question 13.

-2x (x + y) + x2
Answer

– 2x (x + y) + x2

= -2x × x + (-2x)y + x2

= – 2x2 – 2xy + x2

= – 2x2 + x2 – 2xy = – x2 – 2xy

Question 14.

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-f14
Answer

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-f14

= b × 2b – b × (1/b) – 2b×b+2b×(1/b)

= 2b2 – 1 – 2b2 + 2

= 2b2 – 2b2 – 1 + 2

= 1

Question 15.

8 (2a + 3b – c) – 10 (a + 2b + 3c)
Answer

8 (2a + 3b – c) – 10 (a + 2b + 3c)

= 16a + 24b – 8c – 10a – 20b- 30c

= 16a – 10a + 24b – 20b – 8c – 30c

= 6a + 4b – 38c

Question 16.

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-f16

Answer

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-f16

= a2 + 1 – b2 + 1 – c2 – 1

= a2 – b2 – c2 + 1

Question 17.

5 x (2x + 3y) – 2x (x – 9y)
Answer

5 x (2x + 3y) – 2x (x – 9y)

= 10x2 + 15xy – 2x2 + 18xy

= 10x2 – 2x2 + 15xy+ 18xy

= 8x2 + 33xy

Question 18.

a + (b + c – d)
Answer

a + (b + c – d)

= a + (b + c – d)

= a + b + c – d

Question 19.

5 – 8x – 6 – x
Answer

5 – 8x – 6 – x

= 5 – 6 – 8x – x

= -1 – 7x

Question 20.

2a + (6- \overline { a-b } )
Answer

2a + (6- \overline { a-b } )

= 2a + (b – a + b)

= 2a + b – a + b

= a + 2b

Question 21.

3x + [4x – (6x – 3)]
Answer

3x + [4x – (6x – 3)]

= 3x + [4x – 6x + 3]

= 3x + 4x – 6x + 3

= 3x + 4x – 6x + 3

= 7x – 6x + 3

= x + 3

Question 22.

5b – {6a + (8 – b – a)}
Answer

5b – {6a + (8 – b – a)}

= 5b – 6a – 8 + b + a

= -6a + a + 5b +b – 8

= -5a + 6b – 8

Question 23.

2x-[5y- (3x -y) + x]
Answer

2x – [5y – (3x – y) + x]

= 2x – {5y – 3x +y + x}

= 2x – 5y + 3x -y – x

= 2x + 3x – x – 5y – y

= 4x – 6y

Question 24.

6a – 3 (a + b – 2)
Answer

6a – 3 (a + b – 2)

= 6a – 3a – 3b + 6

= 3a – 3b + 6

Question 25.

8 [m + 2n-p – 7 (2m -n + 3p)]
Answer

8 [m + 2n – p – 7 (2m – n + 3p)]

= 8 [m + 2n – p- 14m + 7n – 21p]

= 8m+ 16n – 8p – 112m + 56n – 168p

= 8m – 112m + 16n + 56n – 8p – 168p

= -104m + 72n – 176p

Question 26.

{9 – (4p – 6q)} – {3q – (5p – 10)}
Answer

{9 – (4p – 6q)} – {3q – (5p – 10)}

= {9 – 4p + 6q} – {3q -5p+ 10}

= 9 – 4p + 6q – 3q + 5p – 10

= 9 – 4p + 5p + 6q – 3q – 10

= p + 3q – 1

Question 27.

2 [a – 3 {a + 5 {a – 2) + 7}]
Answer

2 [a – 3 {a + 5 {a – 2) + 7}]

= 2 [a – 3 {a + 5a – 10 + 7}]

= 2 [a – 3a – 15a + 30 – 21]

= 2a – 6a – 30a + 60 – 42

= 2a – 36a + 60 – 42

= -34a + 18

Question 28.

5a – [6a – {9a – (10a – \overline { 4a-3a }  )}]
Answer

5a – [6a – {9a – (10a – \overline { 4a-3a }  )}]

= 5a – [6a – {9a – (10a – 4a + 3a)}]

= 5a – [6a – {9a – 10a + 4a – 3a}]

= 5a- [6a – 9a + 10a – 4a + 3a]

= 5a – 6a + 9a – 10a + 4a – 3a

= 5a + 9a + 4a – 6a – 10a – 3a

= 18a – 19a

= – a

Question 29.

9x + 5 – [4x – {3x – 2 (4x – 3)}]
Answer

9x + 5 – [4x – {3x – 2 (4x – 3)}]

= 9x + 5 – [4x – {3x – 8x + 6}]

= 9x + 5 – [4x – 3x + 8x – 6]

= 9x + 5-4x + 3x – 8x + 6

= 9x + 3x – 4x – 8x + 5 + 6

= 12x – 12x + 11

= 11

Question 30.

(x + y – z)x + (z + x – y)y – (x + y – z)z

Answer

(x + y – z)x + (z + x – y)y – (x + y – z)z

= x2+ xy – zx + yz + xy -y2 – zx – yz + z2

= x2 – y2 + z2 + 2xy – 2zx

Question 31.

-1 [a-3 {b -4 (a-b-8) + 4a} + 10]
Answer

-1 [a – 3 {b – 4 (a – b – 8) + 4a} + 10]

= -1 [a – 3 {b – 4{a – b – 8) + 4a} + 10]

= -1[a – 3 {b – 4a + Ab +32 + 4a} + 10]

= -1 [a – 3b + 12a – 126 – 96 – 12a + 10]

= -a + 3b – 12a + 12b + 96 + 12a – 10

= -a-12a + 12a+ 3b+ 12b – 96 – 10

= – a + 15b – 106

Question 32.

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-f32
Answer

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-f32

Exe - 11 Soved Questions of Fundamental Concepts for ICSE Class-7 img 59

Question 33.

10 – {4a – (7 – \overline { a-5 }) – (5a – \overline { 1+a })}
Answer

10 – {4a – (7 – \overline { a-5 }) – (5a – \overline { 1+a })}

= 10 – {4a – (7 – a + 5) – (5a – 1 – a)}

= 10- {4a -(12 – a) -(4a – 1)}

= 10 – {4a – 12 + a- 4a + 1}

= 10 – 4a + 12 – a + 4a – 1

= 10 + 12 – 1 – 4a – a + 4a

= 21 – a

Question 34.

7a- [8a- (11a-(12a- \overline { 6a-5a })}]
Answer

7a- [8a- (11a-(12a- \overline { 6a-5a })}]

= 7a – [8a – {11a – (12a – 6a + 5a)}]

= 7a – [8a – {11a – (17a – 6a)}]

= 7a – [8a – {11a – (11a)}]

= 7a – [8a – {11a – 11a}]

= 7a – 8a

= – a

Question 35.

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-f35
Answer

Selina Concise Mathematics class 7 ICSE Solutions - Fundamental Concepts (Including Fundamental Operations)-f35

= 8x – [4y – {4x + (2x – 2y + 2x)}]

= 8x – [4y – {4x + (4x – 2y)}]

= 8x – [4y – {4x + 4x – 2y}]

= 8x – [4y – {4x – 4x + 2y}]

= 8x – [- 8x + 6y]

= 8x + 8x – 6y

= 16x – 6y

Question 36.

x-(3y- \overline { 4z-3x } +2z- \overline { 5y-7x })
Answer

x-(3y- \overline { 4z-3x } +2z- \overline { 5y-7x })

= x – (3y – 4z + 3x + 2z -5y + 7x)

= x – (- 2y – 2z + 10x)

= x + 2y + 2z – 10x

= – 9x + 2y + 2z

— End of Fundamental Concepts Solutions :–

Return to – Concise Selina Maths Solutions for ICSE Class -7 


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